Expand the Trigonometric Expression (z+2)^2

${(z + 2)}^{2}$

Step 1

Rewrite ${(z + 2)}^{2}$ as $(z + 2) (z + 2)$ .

$(z + 2) (z + 2)$

Step 2

Expand $(z + 2) (z + 2)$ using the FOIL Method.

Apply the distributive property.

$z (z + 2) + 2 (z + 2)$

Apply the distributive property.

$z \cdot z + z \cdot 2 + 2 (z + 2)$

Apply the distributive property.

$z \cdot z + z \cdot 2 + 2 z + 2 \cdot 2$

$z \cdot z + z \cdot 2 + 2 z + 2 \cdot 2$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $z$ by $z$ .

$z^{2} + z \cdot 2 + 2 z + 2 \cdot 2$

Move $2$ to the left of $z$ .

$z^{2} + 2 \cdot z + 2 z + 2 \cdot 2$

Multiply $2$ by $2$ .

$z^{2} + 2 z + 2 z + 4$

$z^{2} + 2 z + 2 z + 4$

Add $2 z$ and $2 z$ .

$z^{2} + 4 z + 4$

$z^{2} + 4 z + 4$

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